A strain wave gearing typically has an annular rigid internally toothed gear, a flexible externally toothed gear disposed coaxially therein, and a wave generator fitted further therein. There are flexible externally toothed gears called “flat-shaped,” “cup-shaped,” and “silk hat-shaped.” A flat-shaped flexible externally toothed gear has a configuration in which the external teeth are formed on a circular outer perimeter surface of a flexible cylindrical part. Cup-shaped and silk hat-shaped flexible externally toothed gears have a flexible cylindrical part, a disk-form diaphragm extending in the radial direction from the rear end of the cylindrical part, and external teeth formed on a portion of the outer perimeter surface on a front end opening side of the cylindrical part. The portion of the front end opening side of the cylindrical part of the flexible externally toothed gear is flexed by the wave generator in a noncircular, generally ellipsoidal form, and the external teeth engage with the internal teeth of the internally toothed gear at both ends in the major axis direction of the ellipsoidal curve.
In a cup-shaped flexible externally toothed gear, the diaphragm extends inward in the radial direction from the cylindrical part, and a boss is integrally formed on an inner perimeter edge of the diaphragm. In a silk hat-shaped flexible externally toothed gear, the diaphragm spreads outward in the radial direction from the cylindrical part, and an annular boss is integrally formed on an outer perimeter edge of the diaphragm.
In a flexible externally toothed gear of any shape, the cylindrical part where the external teeth are formed is repeatedly flexed in the radial direction by the wave generator. In a cup-shaped or silk hat-shaped flexible externally toothed gear, the portion of the front end opening side where the external teeth are formed on the cylindrical part is ellipsoidally flexed by the wave generator. Therefore, in the ellipsoidally flexed state when cut in cross section including the major axis of the ellipsoidal curve, the amount of flexing of the cylindrical part of the flexible externally toothed gear gradually increases from the diaphragm-side end to the front end opening following the tooth trace direction of the external teeth. Conversely, when cut in cross section including the minor axis of the ellipsoidal curve, the amount of flexing gradually decreases from the diaphragm-side end to the front end opening. Accordingly, a flexing motion called “coning,” in which the front end opening-side is repeatedly flexed outward and inward in the radial direction centered on the diaphragm-side end, occurs on each portion of the flexible externally toothed gear accompanying rotation of the wave generator.
The wave generator for ellipsoidally flexing the flexible externally toothed gear generally has a structure in which a cam plate including a rigid body having an ellipsoidal contour is fitted by way of ball bearings into front end opening of the cylindrical part of the flexible externally toothed gear. The ball bearings are called “wave bearings,” and an outer wheel and an inner wheel thereof can flex in the radial direction. There is also known a wave generator that is configured so that the flexible externally toothed gear is ellipsoidally flexed using a piezoelectric element instead of a cam plate having an ellipsoidal contour. Strain wave gearings having this form of wave generator are disclosed in patent documents 1 and 2.
Meanwhile, there is also known and described in patent document 2 a friction-coupling strain wave apparatus for performing a decelerating operation using the same principle as a strain wave gearing. In this kind of friction-coupling strain wave apparatus as well, a flexible ring thereof is flexed in the radial direction by a wave generator, and each part of the flexible ring is repeatedly flexed in the radial direction accompanying rotation of the wave generator.